l2hmc 0.13.0

Framework for training MCMC samplers for Lattice QCD

Contents

• Overview
  • Papers 📚, Slides 📊, etc.
  • Background
• Installation
• Training
• Details
  • L2HMC for LatticeQCD
  • Organization
    • Dynamics / Network
      • Network Architecture
    • Lattice

Overview

Papers 📚, Slides 📊, etc.

• 📘 Example Notebook (alternative link if github won't load)
• Accelerated Sampling Techniques for Lattice Gauge Theory @ BNL & RBRC: DWQ @ 25 (12/2021)
• Training Topological Samplers for Lattice Gauge Theory from the ML for HEP, on and off the Lattice @ $\mathrm{ECT}^{*}$ Trento (09/2021) (+ 📊 slides)
• Deep Learning Hamiltonian Monte Carlo @ Deep Learning for Simulation (SimDL) Workshop ICLR 2021
  • 📚 : arXiv:2105.03418
  • 📊 : poster

Background

The L2HMC algorithm aims to improve upon HMC by optimizing a carefully chosen loss function which is designed to minimize autocorrelations within the Markov Chain, thereby improving the efficiency of the sampler.

A detailed description of the original L2HMC algorithm can be found in the paper:

Generalizing Hamiltonian Monte Carlo with Neural Network

with implementation available at brain-research/l2hmc/ by Daniel Levy, Matt D. Hoffman and Jascha Sohl-Dickstein.

Broadly, given an analytically described target distribution, π(x), L2HMC provides a statistically exact sampler that:

• Quickly converges to the target distribution (fast burn-in).
• Quickly produces uncorrelated samples (fast mixing).
• Is able to efficiently mix between energy levels.
• Is capable of traversing low-density zones to mix between modes (often difficult for generic HMC).

Installation

• l2hmc on PyPi:

$ python3 -m pip install l2hmc

Training

This project uses hydra for configuration management and supports distributed training for both PyTorch and TensorFlow.

The l2hmc/conf/config.yaml contains a brief explanation of each of the various parameter options, and values can be overriden either by modifying the config.yaml file, or directly through the command line, e.g.

cd src/l2hmc
./train.sh mode=debug framework=pytorch > train.log 2>&1 &
tail -f train.log $(tail -1 logs/latest)

for more information on how this works I encourage you to read Hydra's Documentation Page.

Details

L2HMC for LatticeQCD

Goal: Use L2HMC to efficiently generate gauge configurations for calculating observables in lattice QCD.

A detailed description of the (ongoing) work to apply this algorithm to simulations in lattice QCD (specifically, a 2D U(1) lattice gauge theory model) can be found in arXiv:2105.03418.

Organization

Dynamics / Network

For a given target distribution, π(x), the Dynamics object (src/l2hmc/dynamics/) implements methods for generating proposal configurations (x' ~ π) using the generalized leapfrog update.

This generalized leapfrog update takes as input a buffer of lattice configurations x and generates a proposal configuration x' = Dynamics(x) by evolving generalized L2HMC dynamics.

Network Architecture

An illustration of the leapfrog layer updating (x, v) --> (x', v') can be seen below.

Contact

Code author: Sam Foreman

Pull requests and issues should be directed to: saforem2

Citation

If you use this code or found this work interesting, please cite our work along with the original paper:

@misc{foreman2021deep,
      title={Deep Learning Hamiltonian Monte Carlo}, 
      author={Sam Foreman and Xiao-Yong Jin and James C. Osborn},
      year={2021},
      eprint={2105.03418},
      archivePrefix={arXiv},
      primaryClass={hep-lat}
}

@article{levy2017generalizing,
  title={Generalizing Hamiltonian Monte Carlo with Neural Networks},
  author={Levy, Daniel and Hoffman, Matthew D. and Sohl-Dickstein, Jascha},
  journal={arXiv preprint arXiv:1711.09268},
  year={2017}
}

Acknowledgement

This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under contract DE_AC02-06CH11357. This work describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the work do not necessarily represent the views of the U.S. DOE or the United States Government.